scholarly journals A Linear-Time Algorithm for Computing K-Terminal Reliability in Series-Parallel Networks

1985 ◽  
Vol 14 (4) ◽  
pp. 818-832 ◽  
Author(s):  
A. Satyanarayana ◽  
R. Kevin Wood
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Parallel Networks ◽  
In Series ◽  
Terminal Reliability

Note on: “A Linear-Time Algorithm for Computing K-Terminal Reliability in Series-Parallel Network”

1996 ◽  
Vol 25 (2) ◽  
pp. 290-290
Author(s):  
A. Satyanarayana ◽  
R. K. Wood ◽  
L. Camarinopoulos ◽  
G. Pampoukis
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
In Series ◽  
Parallel Network ◽  
Terminal Reliability

scholarly journals A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs

2017 ◽  
Vol 2017 ◽  
pp. 1-4 ◽  
Author(s):  
Brahim Chaourar
Keyword(s):  
Linear Time ◽  
Maximum Flow ◽  
Time Algorithm ◽  
Minimum Cut ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Positive Weight ◽  
Max Cut Problem ◽  
In Series ◽  
Minimum Cut Problem

Given a graph G=V,E, a connected sides cut U,V\U or δU is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs GU and GV\U are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut Ω such that wΩ is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

A Linear time algorithm for deciding security

1976 ◽  
Author(s):  
A. K. Jones ◽  
R. J. Lipton ◽  
L. Snyder
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm
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